Dance Mathematics: Rhythms and Dances; Analysis and Synthesis

This book is aimed at* Choreographers and teachers * Dancers* Mathematicians* Critics, writers and researchers wishing to further their insights into the dance. These understandings are obtained from mathematical associations not readily perceived, yet quite intrinsic to a piece.Features are* Many simple examples showing the arithmetic that leads to a piece's characterization or to choreographing all or part of a piece* Illustrations that visually facilitate understanding a concept* Historical precedents where mathematical applications relate to the world of dance Benefits to the reader are expanding perception and creative abilities by* Computing numbers that supplement dance characterizations that hitherto using only words* Finding features in a piece otherwise hidden or possibly never considered as a feature* Giving synthesizing aids for rhythms and dances that use a numerical approach in creating a piece Added insights can become aids to creativity. Here mathematics is another tool for the dancer and choreographer to explore improvements in their works. In this respect there are both analysis and synthesis applications. For the former the structure of a specific rhythm or dance is first detailed as a sequence of numbers for input to mathematical procedures. Calculations then analyze these and give numerical results for many features found.Examples are very extensively used. Here historically used notations, reviewed somewhat, do not lend themselves to the numerical manipulations of this book. Hence varieties of digital notations are put forward. The rhythmic aspect of the dance, being simplest to explore in early chapters, can be notated as a sequence of numbers. It is shown how simple arithmetic can analyze to extract features of the rhythm. It becomes apparent how these impartial numbers as answers supplement traditional characterizations that use words whose precise meaning can vary among speakers.The analysis techniques demonstrated for rhythms are used on simplified dance examples. Concepts of feature extractions again can be understood in these. But there is recognition that a much more detailed input of numerical information is ultimately needed for the dance compared to that for rhythms. Aspects of characterizing a dance with numerical analysis then as a consequence can exhibit numerous possibilities compared to rhythms. Describing how results from analysis may be used in aids to synthesizing rhythms and dances are a major part of the book. Simple examples using just numbers illustrate how synthesizing using a computer, with its substantial detail handling capabilities, can reasonably simulate and even create styles. In one of these the reader can follow a path through a flow chart for tap dance synthesis as if it were a board game. Simple calculations at stopping points in the chart make decisions and give sequential dance steps as output results. Thus synthesizing aids have come a long way from the days of Mozart. He rolled dice to achieve randomness in decision making in some of his experimental compositions. Included in variety of references particularly are those showing roles of computers in the subject matter of this book. Here this second edition of this book differs significantly from the first when computers had barely arrived. The first edition shows how a 1500 lb early generation computer struggled to synthesize a short beginners tap dance routine. This second edition reports that, with modern computer data handling capabilities, ballet pieces with their numerous dancer movements have been successfully synthesized. Thus it can be hoped that this book may become another step in an ongoing process in the development of selected facets of the dance.

Author: Joseph Thie

Publisher: CreateSpace Independent Publishing Platform

Publication Date: Sep 21, 2018

Number of Pages: 94 pages

Language: English

Binding: Paperback

ISBN-10: 1723420883

ISBN-13: 9781723420887